Faster Algorithms for the Shortest Path Problem (Classic Reprint) - Softcover

Ahuja, Ravindra K.

Softcover

ISBN 10: 1332260764 ISBN 13: 9781332260768

Verlag: Forgotten Books, 2018

Inhaltsangabe

Excerpt from Faster Algorithms for the Shortest Path Problem

Surprisingly, these two directions have not been very complementary. The algorithms that achieve the best worst-case complexity have generally not been attractive empirically and the algorithms that have performed well in practice have generally failed to have an attractive worst-case bound. In this paper, we present new implementations of Dijkstra's algorithm intended to bridge this gap. Under the assumption that arc lengths are bounded by a polynomial function of n these algorithms achieve the best possible worst-case complexity for all but very sparse graphs and yet are simple enough to be efficient in practice.

About the Publisher

Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com

This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Über diesen Titel

Reseña del editor

Excerpt from Faster Algorithms for the Shortest Path Problem

In this paper, we present the fastest known algorithms for the shortest path problem with nonnegative integer arc lengths We consider networks with n nodes and m arcs and in which C represents the largest arc length in the network. Our algorithms are obtained by implementing Dijkstra's algorithm using a new data structure which we call a redistributive heap The one-level redistributive heap consists of O(log C) buckets, each with an associated range of integer numbers Each bucket stores nodes whose temporary distance labels lie in its range Further, the ranges are dynamically changed during the execution, which leads to a redistribution of nodes to buckets. The resulting algorithm runs in O(m + n log C) time. Using a two-level redistributive heap, we improve the complexity of this algorithm to O(m + n log C/ log log nC). Finally, we use a modified version of Fibonacci heaps to reduce the complexity of our algorithm to O(m + n √log C ). This algorithm, under the assumption that the largest arc length is bounded by a polynomial function of n, runs in O(m + n√log n ) time, which improves over the best previous strongly polynomial bound of O(m + n log n) due to Fredman and Tarjan. We also analyse our algorithms in the semi-logarithmic model of computation. In this model, it takes [log x/log n] time to perform arithmetic on integers of value x. It is shown that in this model of computation, some of our algorithms run in linear time for sufficiently large values of C.

About the Publisher

Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com

This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Details zur Ausgabe

• Verlag: Forgotten Books
• Erscheinungsdatum: 2018
• Sprache: Englisch
• ISBN 10: 1332260764
• ISBN 13: 9781332260768
• Einband: Tapa blanda
• Anzahl der Seiten: 48
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar